1. Technical Field of the Invention
This invention relates to a method and an apparatus for converting a multi-layer circuit into an equivalent circuit model.
2. Description of Related Art
With the fast development of low loss and high density integrated packaging technologies such as low temperature co-fired ceramic (LTCC), a system on package (SoP) is considered as one of the most promising solutions for integrated electronic systems and hand-held wireless products. In designing an advanced SoP, one of the desired CAD tools is an algorithm that can systematically generate a physically meaningful circuit model for complex multi-layer circuits and interconnections.
Such a tool is mainly needed in: (1) a co-simulation of a mixed-signal heterogeneous system that includes digital circuits, which are usually modeled by a circuit simulator in time domain, and analog passive circuits, which are simulated by an electromagnetic (EM) simulation in frequency domain; and (2) the prediction of an electromagnetic interference (EMI) among multi-layer circuits.
Although tremendous work has been done in EM modeling and the extraction of a circuit representation of an embedded passive at GHz frequencies, circuit models resulted therefrom are limited to a predefined layout or the complexity of the circuit models is still overwhelming even with certain model simplification.
Obviously, it is highly desirable to develop a systematic technique that can directly convert a generic layout of a multi-layer circuit to a concise circuit model that is valid in a given range of frequency. Preferably, the circuit model possesses a clear physical meaning associated with a physical layout.
A number of techniques for extracting a lumped element equivalent circuit model for multi-layer circuit have been developed in the past years. The most popular technique is to construct an equivalent circuit model based on a predefined circuit topology from physical intuition. The component values of the circuit model can be determined by empirical formulas or by curve fitting. However, due to the lack of good understanding of the parasitic coupling mechanism for complex passive layouts, such a circuit model could not be too sophisticated and unique.
It is well known that a partial element equivalent circuit (PEEC) model is evolved from a mixed potential integral equation (MPIE). Although the PEEC model, which is also named as a coupling network in this invention, can be regarded as a primitive equivalent circuit, the number of the circuit elements is excessive to handle for practical cases and the capacitors and inductors in the model are only associated with a computational mesh structure.
The references cited herein are explicitly incorporated by reference in its entirety.